## Nuts in a Bowl

Scattered around the house are 100 nuts in 5 bowls.

- The 1st and 2nd bowls together contain 48 nuts.
- The 2nd and 3rd bowls together contain 34.
- The 3rd and 4th bowls together contain 30.
- The 4th and 5th bowls together contain 48.

Scattered around the house are 100 nuts in 5 bowls.

- The 1st and 2nd bowls together contain 48 nuts.
- The 2nd and 3rd bowls together contain 34.
- The 3rd and 4th bowls together contain 30.
- The 4th and 5th bowls together contain 48.

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18, 30, 4, 26, 22

Hi, Thomas. I’m curious how you figured it out. Could you describe how you started, at least? Thanks!

Thomas is correct

Use algebra to write out each equation Then you will find combinations that can used to solve the main equation.

Algebra is a great way to show the relationships you noticed in the problem. I wonder what relationships people noticed?

You can use algebra but its easier to just add what is in the first and second bowls with what is in the third and fourth to work out what must be in the fifth. Once you know what is in one bowl the rest is straightforward.

A different question:

How many nuts are contained in the 1st and 5th bowls, together?

From the answer already given, we see it is 18+22 = 40.

But is there a quicker way to figure this out from the givens?